The population of a town in 2010 was 8,500 people. The population has decreased by 4.5% each year since.

1. Write an equation showing how to find the population of the town *t *years after 2010.

2. In what year will the population of the town equal 7,000 people? Show your calculations.

Thank you!

Guest May 21, 2018

#1**+2 **

(a) 8,500-4.5%(t)

(b) 2010: 8,500

2011: 8117

2012: 7752

2013: 7403

2014: 7069

2015: 6751

Thus, it'll be \(\boxed{2015}\) , when the population will equal 7000.

tertre May 21, 2018

#2**+1 **

Present population =PP

Future population =FP

FP = PP x [1 - 0.045]^t

7,000 = 8,500 x [0.955]^t divide both sides by 8,500

0.823529... = 0.955^t take the log of both sides

t =Log(0.823529) / Log(0.955)

**t = 4.22 = ~ 4.25 years after 2010 when the population of the town will be about 7,000.**

Guest May 21, 2018

edited by
Guest
May 21, 2018